solve by completing the square x^2-4x+2=0?

x² - 4x + 4 = 4 - 2
(x - 2)² = 2
x + 2 = ± √2
x = - 2 ± √2

x² - 4x+2=0
Subtract 2 from both sides
x² - 4x = -2
Take half of the coefficient of the x-term, and square it. (-2)² = 4.
Add this square to both sides of the equation.
x² - 4x + 4 = -2 + 4
Convert the left-hand side to squared form, and simplify the right-hand side.
(x-2)² = 2
Square-root both sides, remembering the "±" on the right-hand side.
(x-2) = +/- √2
Solve for x
x - 2 = +/- √2
Add 2 to both sides
x = 2 +/- √2
x = 2 + √2 and x = 2 - √2

Check out this site:
http://www.purplemath.com/modules/sqrquad.htm

I hope I helped! Good luck.

use -b+sqrt(b*b-4*a*c) and -b-sqrt(b*b-4*a*c)

x^2 - 4x + 2 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = -4
c = 2

x = [4 ±√(16 - 8)]/2
x = [4 ±√8]/2
x ≈ [4 ±2.82]/2

x ≈ [4 + 2.82]/2
x ≈ 6.82/2
x ≈ 3.41

x ≈ [4 - 2.82]/2
x ≈ 1.18/2
x ≈ 0.59

∴ x ≈ 0.59 , 3.41

x^2 - 4x + 2 + 2 = 2

x^2 - 4x + 4 = 2

(x - 2)^2 = 2

x - 2 = +/- sqrt(2)

x = 2 +/- sqrt(2) <<<<<

You can check this with the quadratic formula as follows.

..........-(-4) +/- sqrt(16 - 8)
x = ...--------------------------------
......................2

...........+4 +/- sqrt(8)
x = ...........................
...................2

Since sqrt(8) = sqrt(4) * sqrt(2) = 2sqrt(2) * for multiplication

.....................4 +/- 2sqrt(2)
we get x = ....--------------------- = 2 +/- sqrt(2) It checks! <<<<<
...........................2

x^2 - 4x + 2 = 0

Move the number (or constant) to the RHS.

x^2 - 4x = -2

Take Half of the coefficient of x.
That means:

-4 (the coefficient of x)
-4/2 = -2 (half of the coefficient of x)

Then, squared it.
(-2)^2 = 4

Add the 4 to both the LHS and RHS.

x^2 - 4x + 4 = -2 + 4

Convert the LHS to squared form.

(x - 2)^2 = 2

Square root both sides:

(x - 2) = ±√2

(Remember the plus and minus sign. Very important)

x = 2 ±√2

So your final answers are 2+√2 and 2 - √2

x² - 4x + 4 = 4 - 2
(x - 2)² = 2
x + 2 = ± √2
x = - 2 ± √2

x^2-4x+2=0
=> x^2-4x+4 = 2
=> (x-2)^2 = 2
=> x-2 = (+ or -) sqrt(2)

x = 2 + sqrt(2) OR 2 - sqrt(2)

x^2-4x+2=0
(x-2)^2 -2=0
(x-2)^2=2
x-2= + or - Square root of 2
x=2 + Square root of 2 or 2 - Square root of 2